1. There are many ways to describe relations and function. Consider the relation shown as a set of ordered pairs:
{(2,3),( −1,5),(4,3),(0,5),(3, −2)}
a. Describe this relation in three different ways:
To describe the given relation in three different ways, you can use the following methods:
1. Listing the ordered pairs: Simply list all the ordered pairs in the relation. For the given relation, it would be:
{(2, 3), (-1, 5), (4, 3), (0, 5), (3, -2)}
2. Describing the relation as a table: Create a table with two columns, one for the input values (also known as the domain) and the other for the corresponding output values (also known as the range or co-domain). Fill in the values from the ordered pairs. For the given relation, it would be:
| Input (Domain) | Output (Range) |
|---------------|--------------|
| 2 | 3 |
| -1 | 5 |
| 4 | 3 |
| 0 | 5 |
| 3 | -2 |
3. Describing the relation as an algebraic expression or a function rule: Identify any patterns or rules that can be applied to obtain the output (range) values from the input (domain) values. In this case, there doesn't seem to be a clear pattern, so you can describe the relation as a set of ordered pairs or a table.
By using these three methods, you can describe the given relation in different ways, giving you a comprehensive understanding of its structure and representation.